Isoperimetric numbers of graph bundles

The main aim of this paper is to give some upper and lower bounds for the isoperimetric numbers of graph coverings or graph bundles, with exact values in some special cases. In addition, we show that the isoperimetric number of any covering graph is not greater than that of the base graph. Mohar's theorem for the isoperimetric number of the cartesian product of a graph and a complete graph can be extended to a more general case: The isoperimetric numberi(G × K_2n) of the cartesian product of any graphG and a complete graphK_2n on even vertices is the minimum of the isoperimetric numberi(G) andn, and it is also a sharp lower bound of the isoperimetric numbers of all graph bundles over the graphG with fiberK_2n. Furthermore, ifn 2i(G) then the isoperimetric number of any graph bundle overG with fibreK_n is equal to the isoperimetric numberi(G) ofG.Partially supported by The Ministry of Education, Korea.